The liquid soap in the mouth is really fucked-up and makes anything I've ever had to put up with out of a teacher seem like nothing. I find it disturbing that it was a special-ed teacher. Definitely someone who should lose a job. If it were my kid that happened to, I'd ask for a parent-teacher conference, and then force soap in the teacher's mouth. (What's good for the goose is good for the gander, as they say.)
Regarding PE coaches and fat bastards... Try an alcoholic PE coach. My last ever PE coach actually stashed bottles above the ceiling tiles. Everybody knew about that shit but he was never fired. I wasn't too worried about him. He was too stupid to pull anything anyway, and too drunk to see ten feet in front of him. I might also mention his nose-picking and once when he stepped away from a urinal in the field house and forgot to put his dick back in his pants first. To hell with him, though, it was the other students in that class I was always worried about. (I think you all know about the volatile mix you get when you combine Aspies and PE class, but I just won't go there tonight.)
Since PE is such bullshit, they should at least give you some options. For example, how about they let you work out at a local dojo after school and you have the sensei sign off on a sheet saying you did indeed burn the requisite number of calories. Bring the sheet back to your school and use the ass-kicking lessons as your PE credit.